Question

(If any are cut off answer what you can see)

3A)

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: H:PA = 0.25; PB = 0.4; Pc = 0.1; PD 0.25 Complete the table. Report all answers accurate to three decimal places. Observed Expected Category Residual Frequency Frequency А 17 B 57 с 8 D 23 What is the chi-square test-statistic for this data? t For significance level alpha 0.1, what is the chi-square Critical Value? Critical Value = What would be the conclusion of this hypothesis test? Fail to reject the Null Hypothesis Reject the Null Hypothesis Report all answers accurate to three decimal places.

3b)

3C)

3D)

Answer 1

a)

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
17	0.250	26.25	-9.25		3.260
57	0.400	42.00	15.00		5.357
8	0.100	10.50	-2.50		0.595
23	0.250	26.25	-3.25		0.402

chi square test statistic,X² = Σ(O-E)²/E =   9.614                      
                          
level of significance, α=   0.01                      
Degree of freedom=k-1=   4   -   1   =   3      
                          
  
                   
                          
Critical value =    6.251 [ Excel function: =chisq.inv.rt(α,df) ]  

   reject Ho                 

b)

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
35	0.200	29.60	5.40		0.985
35	0.200	29.60	5.40		0.985
47	0.300	44.40	2.60		0.152
31	0.300	44.40	-13.40		4.044

chi square test statistic,X² = Σ(O-E)²/E =   6.167                          
                              
level of significance, α=   0.05                          
Degree of freedom=k-1=   4   -   1   =   3          
                              
  
Do not reject Ho                             
                              
                              
Critical value =    7.815   [ Excel function: =chisq.inv.rt(α,df) ]             

       

Please let me know in case of any doubt.

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